A New Linear Interpolation Algorithm

The commonly used linear interpolation methods in the NC system are point by point comparison method, digital integration method and minimum deviation method. All of these interpolation algorithm need operation in each feeding period, which consume CPU time severely, and makes the stepping motor vulnerable to violent vibration. When the ratio of rotational speed of Y-axis motor over that of X-axis motor is identical to the slope of theoretical line, resultant velocity of the speed of the X-axis and the Y-axis is parallel to the theoretical line according to velocity synthesis principle. This paper demonstrated that by using this method, CPU only needed to operate once and can make the velocity of X-axis and the Y-axis unchanged, to complete linear interpolation. In addition, the algorithm error was shown smaller than 1 pulse equivalent by theoretical analysis and MATLAB. By using MATLAB to compare this algorithm presented here with point by point comparison algorithm in terms of speed and interpolation calculation time, it was indicated that the algorithm was promising in industry application.